Taking the kids to Disney World? You bought the tickets,
reserved the hotel, arrived there, and … wooow there are so many things
to do at an amusement park. You do not have time for all of the rides, or do
you? Does it matter whether you ride the SpaceMountain first and then SplashMountain,
or should you start with the Pirates of the Caribbean and finish up with a
visit at SpaceMountain? It turns out that some of
these places are busier at different times and days of the week. According to The Unofficial
Guide to the Walt Disney World, selecting optimal tours is the key to
getting the most out of your visit. On days of heavy attendance, groups who did
not use The Guide ended up spending an average of three and a half hours more
in line and experienced 37% fewer attractions than did those who used the
touring plans suggested by the authors of The Guide.

The 2010 edition of The Guide is part of a series that has
sold over four million copies and devotes an entire chapter (pages 75 through
107) explaining the significance of optimal tours and how they were derived. In
page 76, the authors express their thanks to Nick Sahinidis and his graduate
students “who have contributed a number of exceptionally helpful
studies.” Did Nick take his graduate students to Disney World and come up
with optimal tours? Not really. It turns out that the problem of optimal tours
at Disney World is mathematically identical to certain production scheduling
products. When production in a continuous chemical reactor is switched from one
type of polymer to another, there is an inevitable transition time, during
which the intermediate product satisfies neither the specs of the starting
product nor those of the final product. The intermediate product must be
recycled at a cost proportional to the transition time. In turn, this time depends
on the starting and final products. Sequence-dependent transition times give
rise to interesting optimization problems, as explained in Nick’s paper
[1]. Back in the early 1990s, Nick and his first graduate student, Russ Vander
Wiel, addressed a natural extension of this problem, the case when transition
times depend on sequence as well as the time of the day that the transition
takes place. This, time-dependent traveling salesman problem, became the
subject matter of three papers [2, 3, 4] that, apparently, are acknowledged in
The Guide. Who says research in optimization does not impact the life of
everyday people?